The magnitudes of power of a biconvex lens (refractive index 1.5) and that of a plano-concave lens (refractive index \(=1.7\)) are same. If the curvature of plano-concave lens exactly matches with the curvature of back surface of the biconvex lens, then ratio of radius of curvature of front and back surface of the biconvex lens is ___________ .

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(A) 5 : 2

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\(\left| P _{ A }\right|=\left| P _{ B }\right|\)
\(0.5\left(\frac{1}{ R _1}+\frac{1}{ R _2}\right)=\frac{0.7}{ R _2}\)
\(\frac{5}{ R _1}=\frac{2}{ R _2}\)
\(\frac{ R _1}{ R _2}=\frac{5}{2}\)

Same subject

Match list-\(I\) with list-\(II\):

List-\(I\)	List-\(II\)
\((A)\)Kinetic energy of plant	\((I)\) \(-\frac{\mathrm{GMm}}{\mathrm{a}}\)
\((B)\) Gravaitatioin potentiyal energy of sun -plant system	\((II)\) \(\frac{\mathrm{GMm}}{2 \mathrm{a}}\)
\((C)\)Total mecaniacal energy of palnt	\((III)\) \(\frac{\mathrm{Gm}}{\mathrm{r}}\)
\((D)\)Escap energyat the surface of plant for unit mass object	\((IV)\) \(-\frac{\mathrm{GMm}}{2 \mathrm{a}}\)

(Where \(\mathrm{a}=\) radius of planet orbit, \(\mathrm{r}=\) radius of planet, \(M=\) mass of Sun, \(m=\) mass of planet)
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JEE Mains 2024 Hard

When a light of a given wavelength falls on a metallic surface the stopping potential for photoelectrons is 3.2 V . If a second light having wavelength twice of first light is used, the stopping potential drops to 0.7 V . The wavelength of first light is _________ m .
\(\left( h =6.63 \times 10^{-34} J . s , e =1.6 \times 10^{-19} C , c =3 \times 10^8 m / s \right)\)

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Match the LIST-I with LIST-II

LIST-I	LIST-II
(A) Gravitational constant	(I) \(\left[\mathrm{LT}^{-2}\right]\)
(B) Gravitational potential energy	(II) \(\left[\mathrm{L}^2 \mathrm{~T}^{-2}\right]\)
(C) Gravitational potential	(III) \(\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]\)
(D) Acceleration due to gravity	(IV) \(\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]\)

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